Rigged hand composed of multiple meshes
You need to fix the armature bones to pivot in the center of the arm's ball joints:

Select the mesh and in Edit mode (Tab) select vertices such that the 3d gizmo (the center of selection) is in center of the ball joint:



Snap the 3D Cursor to the selection: Shift S > To Selected

Select the armature object and enter Edit mode, select corresponding joint and snap it to 3D Cursor with Shift S > Selection to Cursor



Do it for every joint. You can also set the bones Roll to align bones rotation axes - place the 3D Cursor to the direction you want the bone to be aligned and Ctrl N > Cursor:


Select the mesh, then shift-select the armature and parent it with Empty bone weights(Ctrl P > With Empty Groups). Now you should see a vertex group for every bone inside mesh data properties tab.

Assign every mesh piece to it's corresponding vertex group. You can select a connected component with Ctrl L:


You are ready to animate.